The paper defines a measure on the set of stable matchings in the marriage problem. This measure is based on the minimization of the envy difference between the sets of men and women, while preserving stability and selects stable matchings with the least conflict of interest between both groups of agents. The solution concept proposed is called Sex-equal Matching (SEM) and the paper also provides an algorithm to compute the set of SEM.

We revisit the concept of fairness in the Student Placement framework. We declare an allocation as α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\upalpha $$\end{document}-equitable if no agent can propose an alternative allocation that nobody else might argue to be inequitable. It turns out that α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\upalpha $$\end{document}-equity is compatible with efficiency. Our analysis fills a gap in the literature by giving normative support to the allocations improving, in terms of (...) efficiency, the Student Optimal Stable allocation. (shrink)

This paper presents a procedure to select equitable stable allocations in two-sided matching markets without side payments. The Equitable set is computed using the Equitable algorithm. The algorithm limits the set of options available for each agent throughout the procedure. The stable matchings selected are generally not extreme, form a lattice and satisfy the condition of being “Ralwsian” in each partition of the market. The Equitable algorithm can also be used to select a particular matching from the Equitable Set favoring (...) particular agents independent of the side of the market to which they belong. (shrink)